I know it's going to be slow using USB 2.0, but I don't have a choice until I buy a new internal HDD.

I created the bootable external USB HDD using OSX.

EDIT:

What does EFI mean? Could this be the USB HDD Startup Disk for OSX?

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EFI is normal, but choosing the startup disk by the 'option' plus restart does not always show all the options since corestorage was introduced. Does the external show up in the System Preferences -> Start up disk?

What does Disk Utility say about the Partition map? Open Disk Utility and select your external disk (not the indented volume on the disk). Should say GUID Partition map.

The other possibility is that a few brands of HDD have not been willing to boot macOS in the past.

Hold down the option key on your keyboard when you go to boot. It should bring up a list of bootable devices. There are a couple odd situations that can cause this to take a long time. If the usb drive does not appear, reset your nvram and try again. This will reset the order in which it checks for bootable devices. All of this requires that the drive itself is bootable and the usb case is functioning properly. I mention the case, because cheap cases often fail. It's typically the usb or firewire bridge that burns out.

EFI is normal, but choosing the startup disk by the 'option' plus restart does not always show all the options since corestorage was introduced. Does the external show up in the System Preferences -> Start up disk?

What does Disk Utility say about the Partition map? Open Disk Utility and select your external disk (not the indented volume on the disk). Should say GUID Partition map.

The other possibility is that a few brands of HDD have not been willing to boot macOS in the past.

PS Are you sure your internal drive is dead?

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The internal HDD that came with the Mac Mini mid 2011 when I originally bought it is definitely dead.

Hold down the option key on your keyboard when you go to boot. It should bring up a list of bootable devices. There are a couple odd situations that can cause this to take a long time. If the usb drive does not appear, reset your nvram and try again. This will reset the order in which it checks for bootable devices. All of this requires that the drive itself is bootable and the usb case is functioning properly. I mention the case, because cheap cases often fail. It's typically the usb or firewire bridge that burns out.

These are all recovery partitions with the possible exception of Macintosh HD (assuming that mounts correctly). Macintosh HD is usually the name of the internal drive, which you indicated was dead. Normally dead drives would fail to show up here. Recovery partitions would not be useful in actually running a system. Beyond that, even if you do get this working, it will be quite slow.

A drive is effectively dead if it won't mount. You can always take it out and and put it back in to make sure it wasn't loose. Apart from that, it should be regarded as dead. 5-6 years is a very old drive.

These are all recovery partitions with the possible exception of Macintosh HD (assuming that mounts correctly). Macintosh HD is usually the name of the internal drive, which you indicated was dead. Normally dead drives would fail to show up here. Recovery partitions would not be useful in actually running a system. Beyond that, even if you do get this working, it will be quite slow.

A drive is effectively dead if it won't mount. You can always take it out and and put it back in to make sure it wasn't loose. Apart from that, it should be regarded as dead. 5-6 years is a very old drive.

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Thanks!

Even if the internal hard drive that came with the Mac Mini mid 2011 is still working I'm better off just replacing it because it's so old it'll die soon?

HDDs don't die due to physical age, there's no reason to think that a drive is going to fail just because it's 5 years old. That's not how it works. If the HDD is still working then keep using it, but as with ANY computer you want to make sure that you have current backups. A drive can fail at ANY time, new or old. The vast majority of my HDD replacements over the years haven't been because the drive is old but because I need the space or because I want a faster drive.

Recovery partition is NOT a full OS. It's just allow you to boot with few limiting functions to diagnosis / restore / repair your Mac. In general, you don't need to touch this partition.

10.12.4 won't make your Mac run faster. To get faster response, you need a SSD (no matter internal or external). You can run external SSD via USB. But if the internal HDD is really dead, just swap that out should be a better choice.

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